Related papers: Quantum variance on quaternion algebras, II
A general method is presented which allows one to determine from the local gauge invariant observables of a quantum field theory the underlying particle and symmetry structures appearing at the lower (ultraviolet) end of the…
We prove the quantum unique ergodicity (QUE) conjecture of Rudnick and Sarnak for the sequence of Pitale lifts, which are Hecke-Maass forms on a congruence quotient of $\mathbb{H}^4$ constructed as lifts from half-integral weight forms…
We study the asymptotic short-distance behaviour as well as the asymptotic large-distance behaviour of the gauge-invariant quark-antiquark nonlocal condensates in QCD. A comparison of some analytical results with the available lattice data…
We develop the relation between hyperbolic geometry and arithmetic equidistribution problems that arises from the action of arithmetic groups on real hyperbolic spaces, especially in dimension up to 5. We prove generalisations of Mertens'…
A class of Fourier based statistics for irregular spaced spatial data is introduced, examples include, the Whittle likelihood, a parametric estimator of the covariance function based on the $L_{2}$-contrast function and a simple…
We review the work of Tosio Kato on the mathematics of non--relativistic quantum mechanics and some of the research that was motivated by this. Topics include analytic and asymptotic eigenvalue perturbation theory, Temple--Kato inequality,…
Variational quantum algorithms offer a promising framework for solving eigenvalue problems on near-term quantum hardware, yet their applicability beyond electronic structure calculations remains relatively unexplored. In this work, we…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
In this paper we study the asymptotic distribution of the cuspidal spectrum of arithmetic quotients of the symmetric space S=SL(n,R)/SO(n). In particular, we obtain Weyl's law with an estimation on the remainder term. This extends results…
We consider the smallest eigenvalue distributions of some Freud unitary ensembles, that is, the probabilities that all the eigenvalues of the Hermitian matrices from the ensembles lie in the interval $(t,\infty)$. This problem is related to…
This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational…
The center of interest in this work are variational problems with integral functionals depending on special nonlocal gradients. The latter correspond to truncated versions of the Riesz fractional gradient, as introduced in [Bellido, Cueto &…
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
Given an m-dimensional compact submanifold $\mathbf{M}$ of Euclidean space $\mathbf{R}^s$, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general $\mathbf{R}^s$-valued functionals…
We discuss a few, apparently different (but actually, tightly related) problems: 1. The relation between QCD and valence quark model, 2. The evaluation of the nonlocal condensate $ \la \bar{q}(x)q(0)\ra $, its relation to heavy-light…
One may ask whether an extended group of invariance can naturally be attributed to the space of associative commutative Quadrahyperbolic Numbers? To search for a rigorous and positive answer to the question, we shall focus on the method of…
We investigate the question of whether or not there exists a noncommutative/ quantum extension of a recent (commutative probabilistic) result of Clarke and Barron. They demonstrated that the Jeffreys' invariant prior of Bayesian theory…
This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
We have constructed a non-relativistic theory of quantum mechanics based on local modulus symmetry. The resulting connection in the covariant derivative is identified as the escape velocity of the gravitational field. A new real and…